Question: Solve for $x$ and $y$ using elimination. ${-2x+3y = 18}$ ${-5x-4y = -47}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${-10x+15y = 90}$ $10x+8y = 94$ Add the top and bottom equations together. $23y = 184$ $\dfrac{23y}{{23}} = \dfrac{184}{{23}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x+3y = 18}\thinspace$ to find $x$ ${-2x + 3}{(8)}{= 18}$ $-2x+24 = 18$ $-2x+24{-24} = 18{-24}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 8}$ into $\thinspace {-5x-4y = -47}\thinspace$ and get the same answer for $x$ : ${-5x - 4}{(8)}{= -47}$ ${x = 3}$